Multiset Canonical Correlation Analysis Research Articles

Fractional-order embedding multiset canonical correlations with applications to multi-feature fusion and recognition

The sample covariance matrices in multiset canonical correlation analysis (MCCA) usually deviate from the true ones owing to noise and the limited number of training samples. In this paper, we thus re-estimate the covariance matrices by using the idea of fractional order embedding to respectively correct sample eigenvalues and singular values. Then, we define fractional-order within-set and between-set scatter matrices, which can significantly reduce the deviation of sample covariance matrices. At last, a novel multiset canonical correlation method is presented for multiset feature fusion, called fractional-order embedding multiset canonical correlations (FEMCCs). The proposed FEMCC method first performs joint feature extraction on multiple sets of feature vectors that are obtained from the same objects, and then fuse the extracted correlation features by a given fusion strategy to form discriminative feature vectors for classification tasks. The proposed method is applied to face recognition and object category classification and is examined using the AR, AT&T, and CMU PIE face image databases and the ETH-80 object database. Numerous experimental results demonstrate the effectiveness and robustness of the FEMCC fusion method.

Multiset Canonical Correlation Analysis Using for Blind Source Separation

To solve the problem of blind source separation, a novel algorithm based on multiset canonical correlation analysis is presented by exploiting the different temporal structure of uncorrelated source signals. In contrast to higher order cumulant techniques, this algorithm is based on second order statistical characteristic of observation signals, can blind separate super-Gaussian and sub-Gaussian signals successfully at the same time with relatively light computation burden. Simulation results confirm that the algorithm is efficient and feasible.

Complex-valued independent vector analysis: Application to multivariate Gaussian model

We consider the problem of joint blind source separation of multiple datasets and introduce a solution to the problem for complex-valued sources. We pose the problem in an independent vector analysis (IVA) framework and provide a new general IVA implementation using Wirtinger calculus and a decoupled nonunitary optimization algorithm to facilitate Newton-based optimization. Utilizing the noncircular multivariate Gaussian distribution as a source prior enables the full utilization of the complete second-order statistics available in the covariance and pseudo-covariance matrices. The algorithm provides a principled approach for achieving multiset canonical correlation analysis.

Joint blind source separation by generalized joint diagonalization of cumulant matrices

In this paper, we show that the joint blind source separation (JBSS) problem can be solved by jointly diagonalizing cumulant matrices of any order higher than one, including the correlation matrices and the fourth-order cumulant matrices. We introduce an efficient iterative generalized joint diagonalization algorithm such that a series of orthogonal procrustes problems are solved. We present simulation results to show that the new algorithms can reliably solve the permutation ambiguity in JBSS and that they offer superior performance compared with existing multiset canonical correlation analysis (MCCA) and independent vector analysis (IVA) approaches. Experiment on real-world data for separation of fetal heartbeat in electrocardiogram (ECG) data demonstrates a new application of JBSS, and the success of the new algorithms for a real-world problem.

Color image canonical correlation analysis for face feature extraction and recognition

Canonical correlation analysis (CCA) is a powerful statistical analysis technique, which can extract canonical correlated features from two data sets. However, it cannot be directly used for color images that are usually represented by three data sets, i.e., red, green and blue components. Current multi-set CCA (mCCA) methods, on the other hand, can only provide the iterative solutions, not the analytical solutions, when processing multiple data sets. In this paper, we develop the CCA technique and propose a color image CCA (CICCA) approach, which can extract canonical correlated features from three color components and provide the analytical solution. We show the mathematical model of CICCA, prove that CICCA can be cast as solving three eigen-equations, and present the realization algorithm of CICCA. Experimental results on the AR and FRGC-2 public color face image databases demonstrate that CICCA outperforms several representative color face recognition methods.

Functional connectivity analysis of fMRI data based on regularized multiset canonical correlation analysis

In this paper we describe a method for functional connectivity analysis of fMRI data between given brain regions-of-interest (ROIs). The method relies on nonnegativity constrained- and spatially regularized multiset canonical correlation analysis (CCA), and assigns weights to the fMRI signals of the ROIs so that their representative signals become simultaneously maximally correlated. The different pairwise correlations between the representative signals of the ROIs are combined using the maxvar approach for multiset CCA, which has been shown to be equivalent to the generalized eigenvector formulation of CCA. The eigenvector in the maxvar approach gives an indication of the relative importance of each ROI in obtaining a maximal overall correlation, and hence, can be interpreted as a functional connectivity pattern of the ROIs. The successive canonical correlations define subsequent functional connectivity patterns, in decreasing order of importance. We apply our method on synthetic data and real fMRI data and show its advantages compared to unconstrained CCA and to PCA. Furthermore, since the representative signals for the ROIs are optimized for maximal correlation they are also ideally suited for further effective connectivity analyses, to assess the information flows between the ROIs in the brain.

Group Study of Simulated Driving fMRI Data by Multiset Canonical Correlation Analysis

In this work, we apply a novel statistical method, multiset canonical correlation analysis (M-CCA), to study a group of functional magnetic resonance imaging (fMRI) datasets acquired during simulated driving task. The M-CCA method jointly decomposes fMRI datasets from different subjects/sessions into brain activation maps and their associated time courses, such that the correlation in each group of estimated activation maps across datasets is maximized. Therefore, the functional activations across all datasets are extracted in the order of consistency across different dataset. On the other hand, M-CCA preserves the uniqueness of the functional maps estimated from each dataset by avoiding concatenation of different datasets in the analysis. Hence, the cross-dataset variation of the functional activations can be used to test the hypothesis of functional-behavioral association. In this work, we study 120 simulated driving fMRI datasets and identify parietal-occipital regions and frontal lobe as the most consistently engaged areas across all the subjects and sessions during simulated driving. The functional-behavioral association study indicates that all the estimated brain activations are significantly correlated with the steering operation during the driving task. M-CCA thus provides a new approach to investigate the complex relationship between the brain functions and multiple behavioral variables, especially in naturalistic tasks as demonstrated by the simulated driving study.

A novel multiset integrated canonical correlation analysis framework and its application in feature fusion

Multiset canonical correlation analysis (MCCA) is difficult to effectively express the integrated correlation among multiple feature vectors in feature fusion. Thus, this paper firstly presents a novel multiset integrated canonical correlation analysis (MICCA) framework. The MICCA establishes a discriminant correlation criterion function of multi-group variables based on generalized correlation coefficient. The criterion function can clearly depict the integrated correlation among multiple feature vectors. Then the paper presents a multiple feature fusion theory and algorithm using the MICCA method. The detailed process of the algorithm is as follows: firstly, extract multiple feature vectors from the same patterns by using different feature extraction methods; then extract multiset integrated canonical correlation features using MICCA; finally form effective discriminant feature vectors through two given feature fusion strategies for pattern classification. The multi-group feature fusion method based on MICCA not only achieves the aim of feature fusion, but also removes the redundancy between features. The experiment results on CENPARMI handwritten Arabic numerals and UCI multiple features database show that the MICCA method has better recognition rates and robustness than the fusion methods based on canonical correlation analysis (CCA) and MCCA.

Nonlinear Blind Source Separation Using Kernel Multi-set Canonical Correlation Analysis

To solve the problem of nonlinear blind source separation (BSS), a novel algorithm based on kernel multi- set canonical correlation analysis (MCCA) is presented. Combining complementary research fields of kernel feature spaces and BSS using MCCA, the proposed approach yields a highly efficient and elegant algorithm for nonlinear BSS with invertible nonlinearity. The algorithm works as follows: First, the input data is mapped to a high-dimensional feature space and perform dimension reduction to extract the effective reduced feature space, translate the nonlinear problem in the input space to a linear problem in reduced feature space. In the second step, the MCCA algorithm was used to obtain the original signals.

Multi-set canonical correlation analysis for the fusion of concurrent single trial ERP and functional MRI

Functional magnetic resonance imaging (fMRI) data and electroencephalography (EEG) data provide complementary spatio-temporal information about brain function. Methods to couple the relative strengths of these modalities usually involve two stages: first forming a feature set from each dataset based on one criterion followed by exploration of connections among the features using a second criterion. We propose a data fusion method for simultaneously acquired fMRI and EEG data that combines these steps using a single criterion for finding the cross-modality associations and performing source separation. Using multi-set canonical correlation analysis (M-CCA), we obtain a decomposition of the two modalities, into spatial maps for fMRI data and a corresponding temporal evolution for EEG data, based on trial-to-trial covariation across the two modalities. Additionally, the analysis is performed on data from a group of subjects in order to make group inferences about the covariation across modalities. Being multivariate, the proposed method facilitates the study of brain connectivity along with localization of brain function. M-CCA can be easily extended to incorporate different data types and additional modalities. We demonstrate the promise of the proposed method in finding covarying trial-to-trial amplitude modulations (AMs) in an auditory task involving implicit pattern learning. The results show approximately linear decreasing trends in AMs for both modalities and the corresponding spatial activations occur mainly in motor, frontal, temporal, inferior parietal, and orbito-frontal areas that are linked both to sensory function as well as learning and expectation—all of which match activations related to the presented paradigm.

Joint Blind Source Separation by Multiset Canonical Correlation Analysis

In this work, we introduce a simple and effective scheme to achieve joint blind source separation (BSS) of multiple datasets using multi-set canonical correlation analysis (M-CCA) [1]. We first propose a generative model of joint BSS based on the correlation of latent sources within and between datasets. We specify source separability conditions, and show that, when the conditions are satisfied, the group of corresponding sources from each dataset can be jointly extracted by M-CCA through maximization of correlation among the extracted sources. We compare source separation performance of the M-CCA scheme with other joint BSS methods and demonstrate the superior performance of the M-CCA scheme in achieving joint BSS for a large number of datasets, group of corresponding sources with heterogeneous correlation values, and complex-valued sources with circular and non-circular distributions. We apply M-CCA to analysis of functional magnetic resonance imaging (fMRI) data from multiple subjects and show its utility in estimating meaningful brain activations from a visuomotor task.

A group study of simulated driving fMRI data by multi-set canonical correlation analysis

A group study of simulated driving fMRI data by multi-set canonical correlation analysis

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<h3>Abstract</h3> Multimodal data fusion is a topic of great interest. Several fusion methods have been proposed to investigate coherent patterns and corresponding linkages across modalities, such as joint independent component analysis (jICA), multiset canonical correlation analysis (mCCA), mCCA+jICA, disjoint subspace using ICA (DS-ICA) and parallel ICA. JICA exploits source independence but assumes shared loading parameters. MCCA maximizes correlation linkage across modalities directly but is limited to orthogonal features. While there is no theoretical limit to the number of modalities analyzed together by jICA, mCCA, or the two-step approach mCCA+jICA, these approaches can only extract common features and require the <i>s</i>a<i>me</i> number of sources/components for all modalities. On the other hand, DS-ICA and parallel ICA can identify both common and distinct features but are limited to two modalities. DS-ICA assumes shared loading parameters among common features, which works well when links are strong. Parallel ICA simultaneously maximizes correlation between modalities and independence of sources, while allowing different number of sources for each modality. However, only a very limited number of modalities and linkage pairs can be optimized. To overcome these limitations, we propose aNy-way ICA, a new model to simultaneously maximize the independence of sources and correlations across modalities. aNy-way ICA combines infomax ICA and Gaussian independent vector analysis (IVA-G) via a shared weight matrix model without orthogonality constraints. Simulation results demonstrate that aNy-way ICA not only accurately recovers sources and loadings, but also the true covariance/linkage patterns, whether different modalities have the same or different number of sources. Moreover, aNy-way ICA outperforms mCCA and mCCA+jICA in terms of source and loading recovery accuracy, especially under noisy conditions. <h3>Clinical Relevance</h3> This establishes a model for N-way data fusion of any number of modalities and linkage pairs, allowing different number of non-orthogonal sources for different modalities.